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Toru Kitagawa

Publications and source records attributed to Toru Kitagawa.

At least 19 recordsLinked to original sources
arXiv2025

Identification-aware Markov chain Monte Carlo

Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the lack of identification leaves a challenge for modern Bayesian computation. Sampling methods often struggle with slow or non-convergence when dealing with multiple modes or flat regions of the target distributions. This paper develops a novel Markov chain Monte Carlo (MCMC) approach for non-identified models, leveraging the knowledge of observationally equivalent sets of parameters, and highlights an important role that identification plays in modern Bayesian analysis. We show that our identification-aware proposal eliminates mode entrapment, achieving a convergence rate uniformly bounded away from zero, in sharp contrast to the exponentially decaying rates characterizing standard Random Walk Metropolis and Hamiltonian Monte Carlo. Simulation studies show its superior performance compared to other popular computational methods including Hamiltonian Monte Carlo and sequential Monte Carlo. We also demonstrate that our method uncovers non-trivial modes in the target distribution in a structural vector moving-average (SVMA) application.

econ.EM↗
arXiv2025

Who With Whom? Learning Optimal Matching Policies

There are many economic contexts where the productivity and welfare performance of institutions and policies depend on who matches with whom. Examples include caseworkers and job seekers in job search assistance programs, medical doctors and patients, teachers and students, attorneys and defendants, and tax auditors and taxpayers, among others. Although reallocating individuals through a change in matching policy can be less costly than training personnel or introducing a new program, methods for learning optimal matching policies and their statistical performance are less studied than methods for other policy interventions. This paper develops a method to learn welfare optimal matching policies for two-sided matching problems in which a planner matches individuals based on the rich set of observable characteristics of the two sides. We formulate the learning problem as an empirical optimal transport problem with a match cost function estimated from training data, and propose estimating an optimal matching policy by maximizing the entropy regularized empirical welfare criterion. We derive a welfare regret bound for the estimated policy and characterize its convergence. We apply our proposal to the problem of matching caseworkers and job seekers in a job search assistance program, and assess its welfare performance in a simulation study calibrated with French administrative data.

econ.EM↗
arXiv2025

Leave No One Undermined: Policy Targeting with Regret Aversion

While the importance of personalized policymaking is widely recognized, fully personalized implementation remains rare in practice, often due to legal, fairness or cost concerns. We study the problem of policy targeting for a regret-averse planner when training data gives a rich set of observables while the assignment rules can only depend on its subset. Our regret-averse criterion reflects a planner's concern about regret inequality across the population. This, in general, leads to a fractional optimal rule due to treatment effect heterogeneity beyond the average treatment effects conditional on the subset of observables. We propose a debiased empirical risk minimization approach to learn the optimal rule from data and establish favorable, new upper and lower bounds for the excess risk, indicating a convergence rate of 1/n and asymptotic efficiency in certain cases. We apply our approach to the National JTPA Study and the International Stroke Trial.

econ.EM↗
arXiv2025

Locally- but not Globally-identified SVARs

This paper analyzes Structural Vector Autoregressions (SVARs) where identification of structural parameters holds locally but not globally. In this case there exists a set of isolated structural parameter points that are observationally equivalent under the imposed restrictions. Although the data do not inform us which observationally equivalent point should be selected, the common frequentist practice is to obtain one as a maximum likelihood estimate and perform impulse response analysis accordingly. For Bayesians, the lack of global identification translates to non-vanishing sensitivity of the posterior to the prior, and the multi-modal likelihood gives rise to computational challenges as posterior sampling algorithms can fail to explore all the modes. This paper overcomes these challenges by proposing novel estimation and inference procedures. We characterize a class of identifying restrictions and circumstances that deliver local but non-global identification, and the resulting number of observationally equivalent parameter values. We propose algorithms to exhaustively compute all admissible structural parameters given reduced-form parameters and utilize them to sample from the multi-modal posterior. In addition, viewing the set of observationally equivalent parameter points as the identified set, we develop Bayesian and frequentist procedures for inference on the corresponding set of impulse responses. An empirical example illustrates our proposal.

econ.EM↗
arXiv2024

Bandit Algorithms for Policy Learning: Methods, Implementation, and Welfare-performance

Static supervised learning-in which experimental data serves as a training sample for the estimation of an optimal treatment assignment policy-is a commonly assumed framework of policy learning. An arguably more realistic but challenging scenario is a dynamic setting in which the planner performs experimentation and exploitation simultaneously with subjects that arrive sequentially. This paper studies bandit algorithms for learning an optimal individualised treatment assignment policy. Specifically, we study applicability of the EXP4.P (Exponential weighting for Exploration and Exploitation with Experts) algorithm developed by Beygelzimer et al. (2011) to policy learning. Assuming that the class of policies has a finite Vapnik-Chervonenkis dimension and that the number of subjects to be allocated is known, we present a high probability welfare-regret bound of the algorithm. To implement the algorithm, we use an incremental enumeration algorithm for hyperplane arrangements. We perform extensive numerical analysis to assess the algorithm's sensitivity to its tuning parameters and its welfare-regret performance. Further simulation exercises are calibrated to the National Job Training Partnership Act (JTPA) Study sample to determine how the algorithm performs when applied to economic data. Our findings highlight various computational challenges and suggest that the limited welfare gain from the algorithm is due to substantial heterogeneity in causal effects in the JTPA data.

econ.EM↗
arXiv2024

SVARs with breaks: Identification and inference

In this paper we propose a class of structural vector autoregressions (SVARs) characterized by structural breaks (SVAR-WB). Together with standard restrictions on the parameters and on functions of them, we also consider constraints across the different regimes. Such constraints can be either (a) in the form of stability restrictions, indicating that not all the parameters or impulse responses are subject to structural changes, or (b) in terms of inequalities regarding particular characteristics of the SVAR-WB across the regimes. We show that all these kinds of restrictions provide benefits in terms of identification. We derive conditions for point and set identification of the structural parameters of the SVAR-WB, mixing equality, sign, rank and stability restrictions, as well as constraints on forecast error variances (FEVs). As point identification, when achieved, holds locally but not globally, there will be a set of isolated structural parameters that are observationally equivalent in the parametric space. In this respect, both common frequentist and Bayesian approaches produce unreliable inference as the former focuses on just one of these observationally equivalent points, while for the latter on a non-vanishing sensitivity to the prior. To overcome these issues, we propose alternative approaches for estimation and inference that account for all admissible observationally equivalent structural parameters. Moreover, we develop a pure Bayesian and a robust Bayesian approach for doing inference in set-identified SVAR-WBs. Both the theory of identification and inference are illustrated through a set of examples and an empirical application on the transmission of US monetary policy over the great inflation and great moderation regimes.

econ.EM↗
arXiv2024

Partially identified heteroskedastic SVARs

This paper studies the identification of Structural Vector Autoregressions (SVARs) exploiting a break in the variances of the structural shocks. Point-identification for this class of models relies on an eigen-decomposition involving the covariance matrices of reduced-form errors and requires that all the eigenvalues are distinct. This point-identification, however, fails in the presence of multiplicity of eigenvalues. This occurs in an empirically relevant scenario where, for instance, only a subset of structural shocks had the break in their variances, or where a group of variables shows a variance shift of the same amount. Together with zero or sign restrictions on the structural parameters and impulse responses, we derive the identified sets for impulse responses and show how to compute them. We perform inference on the impulse response functions, building on the robust Bayesian approach developed for set identified SVARs. To illustrate our proposal, we present an empirical example based on the literature on the global crude oil market where the identification is expected to fail due to multiplicity of eigenvalues.

econ.EM↗
arXiv2024

Adaptive Experimental Design for Policy Learning

This study investigates the contextual best arm identification (BAI) problem, aiming to design an adaptive experiment to identify the best treatment arm conditioned on contextual information (covariates). We consider a decision-maker who assigns treatment arms to experimental units during an experiment and recommends the estimated best treatment arm based on the contexts at the end of the experiment. The decision-maker uses a policy for recommendations, which is a function that provides the estimated best treatment arm given the contexts. In our evaluation, we focus on the worst-case expected regret, a relative measure between the expected outcomes of an optimal policy and our proposed policy. We derive a lower bound for the expected simple regret and then propose a strategy called Adaptive Sampling-Policy Learning (PLAS). We prove that this strategy is minimax rate-optimal in the sense that its leading factor in the regret upper bound matches the lower bound as the number of experimental units increases.

cs.LG↗
arXiv2023

Treatment Choice, Mean Square Regret and Partial Identification

We consider a decision maker who faces a binary treatment choice when their welfare is only partially identified from data. We contribute to the literature by anchoring our finite-sample analysis on mean square regret, a decision criterion advocated by Kitagawa, Lee, and Qiu (2022). We find that optimal rules are always fractional, irrespective of the width of the identified set and precision of its estimate. The optimal treatment fraction is a simple logistic transformation of the commonly used t-statistic multiplied by a factor calculated by a simple constrained optimization. This treatment fraction gets closer to 0.5 as the width of the identified set becomes wider, implying the decision maker becomes more cautious against the adversarial Nature.

econ.EM↗
arXiv2023

Individualized Treatment Allocation in Sequential Network Games

Designing individualized allocation of treatments so as to maximize the equilibrium welfare of interacting agents has many policy-relevant applications. Focusing on sequential decision games of interacting agents, this paper develops a method to obtain optimal treatment assignment rules that maximize a social welfare criterion by evaluating stationary distributions of outcomes. Stationary distributions in sequential decision games are given by Gibbs distributions, which are difficult to optimize with respect to a treatment allocation due to analytical and computational complexity. We apply a variational approximation to the stationary distribution and optimize the approximated equilibrium welfare with respect to treatment allocation using a greedy optimization algorithm. We characterize the performance of the variational approximation, deriving a performance guarantee for the greedy optimization algorithm via a welfare regret bound. We implement our proposed method in simulation exercises and an empirical application using the Indian microfinance data (Banerjee et al., 2013), and show it delivers significant welfare gains.

econ.EM↗
arXiv2023

Asymptotically Optimal Fixed-Budget Best Arm Identification with Variance-Dependent Bounds

We investigate the problem of fixed-budget best arm identification (BAI) for minimizing expected simple regret. In an adaptive experiment, a decision maker draws one of multiple treatment arms based on past observations and observes the outcome of the drawn arm. After the experiment, the decision maker recommends the treatment arm with the highest expected outcome. We evaluate the decision based on the expected simple regret, which is the difference between the expected outcomes of the best arm and the recommended arm. Due to inherent uncertainty, we evaluate the regret using the minimax criterion. First, we derive asymptotic lower bounds for the worst-case expected simple regret, which are characterized by the variances of potential outcomes (leading factor). Based on the lower bounds, we propose the Two-Stage (TS)-Hirano-Imbens-Ridder (HIR) strategy, which utilizes the HIR estimator (Hirano et al., 2003) in recommending the best arm. Our theoretical analysis shows that the TS-HIR strategy is asymptotically minimax optimal, meaning that the leading factor of its worst-case expected simple regret matches our derived worst-case lower bound. Additionally, we consider extensions of our method, such as the asymptotic optimality for the probability of misidentification. Finally, we validate the proposed method's effectiveness through simulations.

cs.LG↗
arXiv2022

Stochastic Treatment Choice with Empirical Welfare Updating

This paper proposes a novel method to estimate individualised treatment assignment rules. The method is designed to find rules that are stochastic, reflecting uncertainty in estimation of an assignment rule and about its welfare performance. Our approach is to form a prior distribution over assignment rules, not over data generating processes, and to update this prior based upon an empirical welfare criterion, not likelihood. The social planner then assigns treatment by drawing a policy from the resulting posterior. We show analytically a welfare-optimal way of updating the prior using empirical welfare; this posterior is not feasible to compute, so we propose a variational Bayes approximation for the optimal posterior. We characterise the welfare regret convergence of the assignment rule based upon this variational Bayes approximation, showing that it converges to zero at a rate of ln(n)/sqrt(n). We apply our methods to experimental data from the Job Training Partnership Act Study to illustrate the implementation of our methods.

econ.EM↗
arXiv2022

Best Arm Identification with Contextual Information under a Small Gap

We study the best-arm identification (BAI) problem with a fixed budget and contextual (covariate) information. In each round of an adaptive experiment, after observing contextual information, we choose a treatment arm using past observations and current context. Our goal is to identify the best treatment arm, which is a treatment arm with the maximal expected reward marginalized over the contextual distribution, with a minimal probability of misidentification. In this study, we consider a class of nonparametric bandit models that converge to location-shift models when the gaps go to zero. First, we derive lower bounds of the misidentification probability for a certain class of strategies and bandit models (probabilistic models of potential outcomes) under a small-gap regime. A small-gap regime is a situation where gaps of the expected rewards between the best and suboptimal treatment arms go to zero, which corresponds to one of the worst cases in identifying the best treatment arm. We then develop the ``Random Sampling (RS)-Augmented Inverse Probability weighting (AIPW) strategy,'' which is asymptotically optimal in the sense that the probability of misidentification under the strategy matches the lower bound when the budget goes to infinity in the small-gap regime. The RS-AIPW strategy consists of the RS rule tracking a target sample allocation ratio and the recommendation rule using the AIPW estimator.

cs.LG↗
arXiv2022

Treatment Choice with Nonlinear Regret

The literature focuses on the mean of welfare regret, which can lead to undesirable treatment choice due to sensitivity to sampling uncertainty. We propose to minimize the mean of a nonlinear transformation of regret and show that singleton rules are not essentially complete for nonlinear regret. Focusing on mean square regret, we derive closed-form fractions for finite-sample Bayes and minimax optimal rules. Our approach is grounded in decision theory and extends to limit experiments. The treatment fractions can be viewed as the strength of evidence favoring treatment. We apply our framework to a normal regression model and sample size calculation.

econ.EM↗
arXiv2022

Policy Choice in Time Series by Empirical Welfare Maximization

This paper develops a novel method for policy choice in a dynamic setting where the available data is a multivariate time series. Overcoming challenges unique to time-series setting such as time-varying environments, history-dependent welfare, dynamic causal effects, and statistical dependence, we propose Time-series Empirical Welfare Maximization (T-EWM) methods. We characterize conditions for T-EWM to consistently learn optimal policies conditional or unconditional on the time-series history, and derive nonasymptotic upper bounds for the welfare regrets. We illustrate a use of T-EWM for optimal restriction rules against Covid-19.

econ.EM↗
arXiv2022

von Mises-Fisher distributions and their statistical divergence

The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasi-Bayesian prior, the von Mises-Fisher distribution is a convenient and parsimonious choice when parameter spaces are isomorphic to the hypersphere (e.g., maximum score estimation in semi-parametric discrete choice, estimation of single-index treatment assignment rules via empirical welfare maximisation, under-identifying linear simultaneous equation models). Despite a long history of application, measures of statistical divergence have not been analytically characterised for von Mises-Fisher distributions. This paper provides analytical expressions for the $f$-divergence of a von Mises-Fisher distribution from another, distinct, von Mises-Fisher distribution in $\mathbb{R}^p$ and the uniform distribution over the hypersphere. This paper also collect several other results pertaining to the von Mises-Fisher family of distributions, and characterises the limiting behaviour of the measures of divergence that we consider.

econ.EM↗
arXiv2021

Paternalism, Autonomy, or Both? Experimental Evidence from Energy Saving Programs

Identifying who should be treated is a central question in economics. There are two competing approaches to targeting - paternalistic and autonomous. In the paternalistic approach, policymakers optimally target the policy given observable individual characteristics. In contrast, the autonomous approach acknowledges that individuals may possess key unobservable information on heterogeneous policy impacts, and allows them to self-select into treatment. In this paper, we propose a new approach that mixes paternalistic assignment and autonomous choice. Our approach uses individual characteristics and empirical welfare maximization to identify who should be treated, untreated, and decide whether to be treated themselves. We apply this method to design a targeting policy for an energy saving programs using data collected in a randomized field experiment. We show that optimally mixing paternalistic assignments and autonomous choice significantly improves the social welfare gain of the policy. Exploiting random variation generated by the field experiment, we develop a method to estimate average treatment effects for each subgroup of individuals who would make the same autonomous treatment choice. Our estimates confirm that the estimated assignment policy optimally allocates individuals to be treated, untreated, or choose themselves based on the relative merits of paternalistic assignments and autonomous choice for individuals types.

econ.GN↗